Non-adiabatic effects of nuclear motion in quantum transport of electrons: A self-consistent Keldysh–Langevin study

Abstract

The molecular junction geometry is modeled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. The time-evolution of the molecular geometry is governed via a mean force, a frictional force, and a stochastic force, forces arising from many electrons tunneling across the junction for a given nuclear vibration. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according to the extended expressions for the current that have explicit dependences on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric current are computed using non-equilibrium Green’s functions via a timescale separation solution of Keldysh–Kadanoff–Baym equations in the Wigner space. Applying the theory to molecular junctions demonstrated that non-adiabatic corrections play an important role when nuclear motion is considered non-equilibrium and, in particular, showed that non-equilibrium and equilibrium descriptions of nuclear motion produce significantly different current characteristics. It is observed that non-equilibrium descriptions generally produce heightened conductance profiles relative to the equilibrium descriptions and provide evidence that the effective temperature is an effective measure of the steady-state characteristics. Finally, we observe that the non-equilibrium descriptions of nuclear motion can give rise to the Landauer blowtorch effect via the emergence of multi-minima potential energy surfaces in conjunction with non-uniform temperature profiles. The Landauer blowtorch effect and its impact on the current characteristics, waiting times, and the Fano factor are explored for an effective adiabatic potential that morphs between a single, double, and triple potential as a function of voltage.

First-passage time theory of activated rate chemical processes in electronic molecular junctions

“…In alignment with our previous work [3,4,32,[56][57][58], we assume that the classical motion along the reaction coordinate within the system occurs over long time-scales relative to the characteristic electron tunnelling time. This provides us with the required small parameter to be able to perturbatively solve ( 5) and ( 6) up to the first order in expansion of the exponents with derivatives.…”

“…Under the overarching assumption that the reaction coordinate x along with its corresponding momentum p are classical variables in our approach due to the separation of time-scales within the system, the equation of motion of the reaction coordinate can be expressed in the form of a quasi-classical Langevin equation, in which the classical motion is dictated by quantum mechanical forces. Our Langevin equation is given by [1,3,4,6,30,31]…”

“…An applied voltage allows for the flow of electronic current across the system through the valence states of the molecule. Large current densities and power dissipation give way to strong current-induced forces and bondselective heating which act to destabilize the molecular configuration within the junction, resulting in molecular conformational changes including telegraphic switching [1][2][3][4], along with providing the necessary energy for total bond rupture [5][6][7][8][9][10][11]. This is obviously an undesirable feature for promoting molecular electronics as a possible avenue for moving beyond the traditional silicon semiconductor technology into a regime of highly efficient and tailorable molecular-scale devices, and so a thorough theoretical understanding is required for further progress.…”

“…This enables the consideration of highly non-trivial behaviour on the nuclear dynamics at the cost of a fully quantum description. Nevertheless, the method has proven successful in a range of circumstances [1,3,4,6,11,[26][27][28][29][30][31][32].…”

Electronic transport in molecular junctions: The generalized Kadanoff-Baym ansatz with initial contact and correlations

“…The device operation is typically ultrafast; there is no guarantee for an instant relaxation to a static configuration once the device is switched on. Emerging transient effects depend on, e.g., quantum dynamics and correlations [6][7][8][9][10][11][12][13][14] , system geometry and topology [15][16][17][18][19][20][21][22] , and the response to external perturbations or thermal gradients [23][24][25][26][27][28][29][30][31][32][33][34][35] . Recently, pump-probe spectroscopic methods have grown in number rapidly leading to the current field of ultrafast materials science with sub-picosecond temporal resolution being routinely achieved [36][37][38][39][40][41][42][43] .…”